Differentiate the following functions. ( -1)( +1) - Vidyadip

Question

Differentiate the following functions.
$(\sec\text{x}-1)(\sec\text{x}+1)$

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Answer

$\frac{\text{d}}{\text{dx}}(\sec\text{x}-1)(\sec\text{x}+1)$
$=(\sec\text{x}-1).\frac{\text{d}}{\text{dx}}(\sec\text{x}+1)+(\sec\text{x}+1)\frac{\text{d}}{\text{dx}}(\sec\text{x}-1)$
$=(\sec\text{x}-1)(\sec\text{x}\tan\text{x})+(\sec\text{x}+1)(\sec\text{x}\tan\text{x})$
$=\sec\text{x}\tan\text{x}(\sec\text{x}-1+\sec\text{x}+1)$
$=\sec\text{x}\tan\text{x}\ 2\sec\text{x}=2\sec\text{x}^{2}.\tan\text{x}$
Hence, the required answer is $2\sec^{2}\text{x}.\tan\text{x}.$

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